3015_Discussion_7_Solutions - University of Minnesota Dept....

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University of Minnesota Dept. of Electrical and Computer Engineering EE3015 – Signals and Systems Discussion Session #7: Fourier Analysis and Synthesis of sounds using Matlab In this discussion, we will numerically analyze and synthesize sounds from different musical instruments using Matlab. This exercise will be graded, and is due next discussion session, Oct. 29-30 . You are required to turn in code and graphs as indicated. This discussion will be devoted to get started with the assignment, but you are expected to finish it outside of class. The submitted work should be your own. You can (and indeed you are encouraged to) discuss this assignment with other students, but the Matlab code you turn in should represent your own individual effort. Preliminaries In this discussion we will use Matlab to find Fourier Series (FS) coefficients of 440Hz pitch sounds from different musical instruments. A 440Hz pitch sound is the musical note A or “concert pitch” and is used as the reference frequency to tune musical instruments. In the discussion website, www.ece.umn.edu/class/ee3015/Discussions.htm you will find a Matlab file “3015_Discussion_7_Matlab.mat” that contains several Matlab vectors. Download this file to your Matlab working folder. You can load the file using Matlab’s load function: >> load 3015_Discussion_7_Matlab If you type whos on Matlab Command Window you will see that Matlab loaded 4 vectors: >> whos Name Size Bytes Class fs 1x1 8 double array oboe 150529x1 1204232 double array piano 176400x1 1411200 double array sax 264600x1 2116800 double array oboe, sax and piano are vectors that represent Concert A sounds. Variable fs is equal to 44100 and is the sampling frequency with which the sounds were captured. Or equivalently, 1/fs is the separation between time samples of the sound. You can hear, for example, oboe by typing (make sure the speakers are on, and output is not muted in Window’s Volume Control): >> sound(oboe,fs)
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3015_Discussion_7_Solutions - University of Minnesota Dept....

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